Happy Long Weekend :)

Hey guys it's "Vince" and according to Mr. P. I'll be doing the blog for the past few days. I'll be discussing with you guys the previous lessons which is: "Solving Exponential and Logarithmic Equations!"

METHOD 1:

STEPS:

1. Simplify the equation to create a proper logarithmic form.
2. Convert the logarithm into exponential form.
3. Solve for the missing variable
4. Check your Answers

For an easier explanation we'll use examples!

Ex.

1 .

* Well first we need to make it in exponent form.

* Oh look we have a negative exponent we'll have to make the exponent positive

* Alright! looks good now, We'll just need to simplify then we'll find out X

So our answer was [1 over 256] to check this we could convert our original equation into an exponent form and then change and plugin [1 over 256] for X and we'll surely get the answer.

2. log(3-x) +1 = log(12-X)

*ohh this is quite hard. but we'll manage. FIRST STEP: SIMPLIFY!

* Put all log on one side then the constant on the other. NOTE: Notice the blue. We can simplify this into one log.

* now we'll convert this to exponential form. Remember since our a is blank that means it's 10. Now we'll cross multiply

See how easy that was after following the steps?

METHOD 2

Steps:

1. Place log with base 10 on each side of the equation.
2. The exponent of becomes the coefficient of the log.
3. If the exponent is in the brackets. multiply through the brackets.
4. Collect log on one side and isolate the variable on the other.
5. Solve for the variable using your calculators. *BEST PART.
6. Check your answers by plugging it to the Xs.

Let's do a hard example on this one. :D

1.

*Step One: Place log with base 10 on each side of the equation.

*notice the blue part, where we changed multiplication into addition(expanding).

*Step Two: The Exponent became the coefficient of the log.

* Since the coefficient is in the bracket we multiply them to the log. Remember: Number to Log = ✔ : Log to Number =

* Step 4: Collect all the log that doesn't have any variable on one side and those that have on the other side. Notice: We can cancel the red part. (-+)

* We can now factor the "x" out so that we can isolate the variable.

* Step 5: Use your calculator and solve for X. Make sure to use brackets on your calculator :)

*Ta-Dah!! Here's your answer :) this is most likely correct. You can try to check it using your calculator by pluging it back.

REFERENCE

So here are some list that anyone can use to study and learn more about logarithms. I use this site a lot and hopefully it would be useful for you guys :)

1. Basic Log Rules / Expanding Logarithmic Expressions
2. Solving Logarithmic Equations
3. Graphing Logarithmic Functions
4. Graphing Exponential Functions

so that was it guys, hope you had a wonderful weekend. If you need help, There are Peer Tutor during lunch at Ms. Russell's Room :) So Visit them out. Hope we have a wonderful week ahead :)

- Vince